Rotated Rectangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

• Rectangle is a quadrilateral with two pair of parallel lines.
• A rotated rectangle is a structural shape used in construction.
• See Geometric Properties of Structural Shapes
• Interior angles are 90°
• Exterior angles are 90°
• Angle $$\;A = B = C = D$$
• 2 diagonals
• 4 edges
• 4 vertexs

Area of a Rotated Rectangle formula

$$\large{ A_{area} = a\;b }$$

Perimeter of a Rotated Rectangle formula

$$\large{ P= 2\; \left( a + b \right) }$$

Side of a Rotated Rectangle formula

$$\large{ a = \frac {P} {2} - b }$$

$$\large{ b = \frac {P} {2} - a }$$

Distance from Centroid of a Rotated Rectangle formula

$$\large{ C_x = \frac { b \; cos \; \theta + a \; sin \; \theta } { 2 } }$$

$$\large{ C_y = \frac { a \; cos \; \theta + b \; sin \; \theta } { 2 } }$$

Elastic Section Modulus of a Rotated Rectangle formula

$$\large{ S_x = \frac { a^2\;b } { 6 } }$$

Polar Moment of Inertia of a Rotated Rectangle formula

$$\large{ J_{z} = \frac {b\;a}{3} \; \left( b^2 + a^2 \right) }$$

Radius of Gyration of a Rotated Rectangle formula

$$\large{ k_{x} = \sqrt{ \frac { a^2 \;cos^2 \; \left( b^2 \; sin^2 \; \theta + \theta \right) } { 2\; \sqrt 3 } } }$$

Second Moment of Area of a Rotated Rectangle formula

$$\large{ I_{x} = \frac {b\;a}{12} \; \left( a^2 \; cos^2 \; \theta + b^2 \; sin^2 \; \theta \right) }$$

Where:

$$\large{ A }$$ = area

$$\large{ a, b }$$ = side

$$\large{ C }$$ = distance from centroid

$$\large{ I }$$ = moment of inertia

$$\large{ J }$$ = torsional constant

$$\large{ k }$$ = radius of gyration

$$\large{ P }$$ = perimeter

$$\large{ S }$$ = elastic section modulus